def example1():
""" unit circle mesh """
def _fd(pts):
""" shape function """
return shape.circle(pts, pc=[0, 0], r=1.)
def _fh(pts):
""" distance function """
r2 = np.sum(pts**2, axis=1)
return 0.2 * (2.0 - r2)
# build fix points, may be used as the position for electrodes
num = 16
p_fix = shape.fix_points_circle(ppl=num)
# firs num nodes are the positions for electrodes
el_pos = np.arange(num)
# build triangle
p, t = distmesh.build(_fd, _fh, pfix=p_fix, h0=0.05)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
ax.plot(p[el_pos, 0], p[el_pos, 1], 'ro')
ax.set_aspect('equal')
ax.set_xlim([-1.5, 1.5])
ax.set_ylim([-1.1, 1.1])
plt.show()
def example_intersect():
"""example on how to use dist_intersect and fix_points_fd"""
def _fd(pts):
""" _fd must centered at [0, 0] """
ellipse = shape.ellipse(pts, pc=[0, -0.6], ab=[1, 1.5])
circle = shape.circle(pts, pc=[0, 0], r=1)
return shape.dist_intersect(ellipse, circle)
# create equal-distributed electrodes
p_fix = shape.fix_points_fd(_fd)
# generate mesh
bbox = [[-2, -2], [2, 2]]
p, t = distmesh.build(_fd,
shape.area_uniform,
pfix=p_fix,
bbox=bbox,
h0=0.1)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
ax.plot(p_fix[:, 0], p_fix[:, 1], 'ro')
ax.set_aspect('equal')
ax.set_xlim([-1.5, 1.5])
ax.set_ylim([-1.2, 1.2])
plt.show()
def example5():
"""
Notes
-----
L-shaped domain from
'Finite Elements and Fast Iterative Solvers'
by Elman, Silvester, and Wathen.
"""
# set fixed points
p_fix = [[1, 0], [1, -1], [0, -1], [-1, -1], [-1, 0], [-1, 1], [0, 1],
[0, 0]]
p_fix = np.array(p_fix)
def _fd(pts):
return shape.dist_diff(shape.rectangle(pts, p1=[-1, -1], p2=[1, 1]),
shape.rectangle(pts, p1=[0, 0], p2=[1, 1]))
# build
p, t = distmesh.build(_fd, shape.area_uniform, pfix=p_fix, h0=0.15)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
ax.plot(p_fix[:, 0], p_fix[:, 1], 'ro')
ax.set_aspect('equal')
ax.set_xlim([-1.2, 1.2])
ax.set_ylim([-1.2, 1.2])
plt.show()
def example1():
""" unit circle mesh """
def _fd(pts):
""" shape function """
return shape.circle(pts, pc=[0, 0], r=1.)
def _fh(pts):
""" distance function """
r2 = np.sum(pts**2, axis=1)
return 0.2*(2.0 - r2)
# build fix points, may be used as the position for electrodes
num = 16
pfix = shape.pfix_circle(numEl=num)
# firs num nodes are the positions for electrodes
epos = np.arange(num)
# build triangle
p, t = distmesh.build(_fd, _fh, pfix=pfix, h0=0.05)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
ax.plot(p[epos, 0], p[epos, 1], 'ro')
plt.axis('equal')
plt.axis([-1.5, 1.5, -1.1, 1.1])
plt.show()
def example_voronoi():
"""draw voronoi plots for triangle elements"""
def _fd(pts):
return shape.dist_diff(shape.circle(pts, r=0.7),
shape.circle(pts, r=0.3))
# build triangle
p, t = distmesh.build(_fd, shape.area_uniform, h0=0.1)
# plot using customized voronoi function
mplot.voronoi_plot(p, t)
def example_voronoi():
"""draw voronoi plots for triangle elements"""
def _fd(pts):
# return d2d.dcircle(pts, pc=[0, 0], r=1.)
return shape.ddiff(shape.circle(pts, r=0.7),
shape.circle(pts, r=0.3))
# build triangle
p, t = distmesh.build(_fd, shape.huniform, h0=0.1)
# plot using customized voronoi function
mplot.voronoi_plot(p, t)
def example2():
"""unit circle with a whole at the center"""
def _fd(pts):
return shape.dist_diff(shape.circle(pts, r=0.7),
shape.circle(pts, r=0.3))
# build triangle
p, t = distmesh.build(_fd, shape.area_uniform, h0=0.1)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
ax.set_aspect('equal')
plt.show()
def example2():
"""unit circle with a whole at the center"""
def _fd(pts):
return shape.ddiff(shape.circle(pts, r=0.7),
shape.circle(pts, r=0.3))
# build triangle
p, t = distmesh.build(_fd, shape.huniform, h0=0.1)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
plt.axis('equal')
plt.show()
def example_voronoi():
"""draw voronoi plots for triangle elements"""
def _fd(pts):
return shape.dist_diff(shape.circle(pts, r=0.9),
shape.circle(pts, r=0.4))
# build triangle
p, t = distmesh.build(_fd, shape.area_uniform, h0=0.1)
# plot using customized voronoi function
_, ax = voronoi_plot(p, t, figsize=(9, 6))
ax.triplot(p[:, 0], p[:, 1], t, color='k', alpha=0.35)
ax.set_aspect('equal')
ax.set_xlim([-1.0, 1.0])
ax.set_ylim([-1.0, 1.0])
plt.show()
def example4():
"""ellipse"""
def _fd(pts):
if pts.ndim == 1:
pts = pts[np.newaxis]
a, b = 2.0, 1.0
return np.sum((pts/[a, b])**2, axis=1) - 1.0
# build triangle
p, t = distmesh.build(_fd, shape.huniform,
bbox=[[-2, -1], [2, 1]], h0=0.15)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
plt.axis('equal')
plt.show()
def example4():
"""ellipse"""
def _fd(pts):
if pts.ndim == 1:
pts = pts[np.newaxis]
a, b = 2.0, 1.0
return np.sum((pts/[a, b])**2, axis=1) - 1.0
# build triangle
p, t = distmesh.build(_fd, shape.area_uniform,
bbox=[[-2, -1], [2, 1]], h0=0.15)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
plt.axis('equal')
plt.show()
def example_dintersect():
"""example on how to use dintersect and pfix_fd"""
def _fd(pts):
""" _fd must centered at [0, 0] """
return shape.dintersect(shape.ellipse(pts, pc=[0, -0.6], ab=[1, 1.5]),
shape.circle(pts, pc=[0, 0], r=1))
# create equal-distributed electrodes
pfix = shape.pfix_fd(_fd)
# generate mesh
bbox = [[-2, -2], [2, 2]]
p, t = distmesh.build(_fd, shape.huniform, pfix=pfix, bbox=bbox, h0=0.1)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
ax.plot(pfix[:, 0], pfix[:, 1], 'ro')
ax.axis('equal')
def example3():
"""rectangle with a whole at the center"""
# interior
def _fd(pts):
return shape.ddiff(shape.rectangle(pts, p1=[-1, -0.6], p2=[1, 0.6]),
shape.circle(pts, r=0.3))
# constraints
def _fh(pts):
return 0.05 + 0.05 * shape.circle(pts, r=0.3)
# build triangle
p, t = distmesh.build(_fd, _fh, h0=0.05)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
ax.set_xlim([-1.2, 1.2])
ax.set_ylim([-1, 1])
plt.show()
def example3():
"""rectangle with a whole at the center"""
# interior
def _fd(pts):
rect = shape.rectangle(pts, p1=[-1, -0.6], p2=[1, 0.6])
circle = shape.circle(pts, r=0.3)
return shape.dist_diff(rect, circle)
# constraints
def _fh(pts):
return 0.05 + 0.05 * shape.circle(pts, r=0.3)
# build triangle
p, t = distmesh.build(_fd, _fh, h0=0.05)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
ax.set_xlim([-1.2, 1.2])
ax.set_ylim([-1, 1])
plt.show()
def example5():
""" L-shaped domain from 'Finite Elements and Fast Iterative Solvers'
by Elman, Silvester, and Wathen. """
# set fixed points
pfix = [[1, 0], [1, -1], [0, -1], [-1, -1],
[-1, 0], [-1, 1], [0, 1], [0, 0]]
pfix = np.array(pfix)
def _fd(pts):
return shape.ddiff(shape.rectangle(pts, p1=[-1, -1], p2=[1, 1]),
shape.rectangle(pts, p1=[0, 0], p2=[1, 1]))
# build
p, t = distmesh.build(_fd, shape.huniform, pfix=pfix, h0=0.15)
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
ax.plot(pfix[:, 0], pfix[:, 1], 'ro')
ax.set_xlim([-1.2, 1.2])
ax.set_ylim([-1.2, 1.2])
plt.show()
def mesh_gen(n_el=20, num_per_el=3):
'''
function that generates the mesh to be used in solving the FEM and inverse problem
takes:
n_el - number of electrodes - int (=20 by default)
returns:
mesh_dict - dictionary of mesh characteristics:
p - array of mesh node coordinates - array shape (number of nodes, 2)
t - indices of triangle vertices in p array (counter-clockwise) - array shape (number of triangles, 3)
el_pos - positions of electrodes on plate (clockwise) - array shape (n_el, 2)
p_fix - coords of fixed points - array shape (number of fixed points, 2)
'''
# defining the shape of the plate (a rectangle of sides a and b)
def _fd(pts):
return shape.rectangle(pts, p1=[-1., -1.], p2=[1., 1.])
# (optional) variable meshing with smaller triangles close to the electrodes - taken by the DISTMESH class (pyEIT)
def _fh(pts):
p_fix, el_pos = fix_electrodes_multiple(edgeX=0.1,
edgeY=0.1,
a=2,
b=2,
ppl=n_el,
el_width=0.2,
num_per_el=num_per_el)
#p_fix, el_pos = fix_points_rectangle(edgeX=0.2, edgeY=0.2, a=2, b=2)
minDist = min_dist_to_el(pts, el_pos)
return 0.45 + 0.3 * np.power(minDist / np.amax(minDist), 2)
# setting the electrodes and fixed points positions in p_fix array
p_fix1, el_pos = fix_electrodes_multiple(edgeX=0.1,
edgeY=0.1,
a=2,
b=2,
ppl=n_el,
el_width=0.2,
num_per_el=num_per_el)
p_fix = np.empty((len(el_pos) + len(p_fix1), 2), dtype='f4')
p_fix[0:len(el_pos)] = el_pos
p_fix[len(el_pos):len(el_pos) + len(p_fix1)] = p_fix1
# building the DISTMESH class object (from pyEIT)
p, t = distmesh.build(_fd, _fh, pfix=p_fix, h0=0.12, maxiter=1000)
# creating the dictionary with the specifics of the meshing
mesh_dict = {'p': p, 't': t, 'el_pos': el_pos, 'p_fix': p_fix}
'''
# plot
fig, ax = plt.subplots()
ax.triplot(p[:, 0], p[:, 1], t)
#ax.plot(p_fix[:, 0], p_fix[:, 1], 'ro')
ax.set_aspect('equal')
#ax.set_xlabel(c0)
#ax.set_ylabel(c1)
ax.set_xlim([-1.2, 1.2])
ax.set_ylim([-1.2, 1.2])
ax.plot(el_pos[:, 0], el_pos[:, 1], 'ro')
plt.show()
'''
# return dictionary
return mesh_dict